How does the brain encode space?

In 2006, a group of researchers published a landmark paper (Sargolini et al. 2006) demonstrating that cells in the hippocampus fired in regular spatial intervals. These researchers, May-Britt & Edvard Moser, were awarded the Nobel Prize in 2014 for their efforts.

This tutorial demonstrates how to access the dataset – the very one they won the Nobel Prize for! – published in using dandi.

The dataset contains spike times for recorded grid cells from the medial entorhinal cortex (MEC) in rats that explored two-dimensional environments. The behavioral data includes position from the tracking LED(s).

Contents:

• Streaming NWB files

• Accessing data and metadata

• Accessing behavior data

• Accessing spike times

• Showing rate maps

Authors

This notebook was authored by Dorota Jareka, Szonja Weigl, and Ben Dichter. It was edited by Ashley Juavinett.

Note #1: The best way to complete this notebook is through the Dandihub. If you’re not already running this book on the Dandihub, read Using this Book for instructions on how to run this on the Dandihub.

---

Streaming NWB files

This section demonstrates how to access the files on DANDI without downloading them. If you need a refresher, we discussed this in Lesson 1. You can also reference the Streaming NWB files tutorial from PyNWB.

The DandiAPIClient can be used to get the S3 URL of this NWB file stored in the DANDI Archive.

from dandi.dandiapi import DandiAPIClient

dandiset_id, nwbfile_path = "000582", "sub-10073/sub-10073_ses-17010302_behavior+ecephys.nwb" # file size ~15.6MB

# Get the location of the file on DANDI
with DandiAPIClient() as client:
    asset = client.get_dandiset(dandiset_id, 'draft').get_asset_by_path(nwbfile_path)
    s3_url = asset.get_content_url(follow_redirects=1, strip_query=True)
    
print(s3_url)

https://dandiarchive.s3.amazonaws.com/blobs/26a/22c/26a22c31-09bc-43a4-9187-edc7394ed12c

Create a virtual filesystem using fsspec which will take care of requesting data from the S3 bucket whenever data is read from the virtual file.

from fsspec.implementations.cached import CachingFileSystem
from fsspec import filesystem
from h5py import File
from pynwb import NWBHDF5IO

# first, create a virtual filesystem based on the http protocol
fs=filesystem("http")

# create a cache to save downloaded data to disk (optional)
fs = CachingFileSystem(
    fs=fs,
    cache_storage="nwb-cache",  # Local folder for the cache
)

file_system = fs.open(s3_url, "rb")
file = File(file_system, mode="r")
# Open the file with NWBHDF5IO
io = NWBHDF5IO(file=file, load_namespaces=True)

nwbfile = io.read()
nwbfile

root (NWBFile)

session_description: This session includes spike and position times for recorded cells from a Long Evans rat that was running in a 1 x 1 meter enclosure. The cells were recorded in the dorsocaudal 25% portion of the medial entorhinal cortex (MEC).Position is given for two LEDs to enable calculation of head direction.

identifier: 294b7de1-a624-44d8-b1a1-28028dd2cf0c

session_start_time

1900-01-01 00:00:00+01:00

timestamps_reference_time

1900-01-01 00:00:00+01:00

file_create_date

0

2023-09-16 15:50:09.775622+02:00

experimenter

('Sargolini, Francesca',)

related_publications

('https://doi.org/10.1126/science.1125572',)

acquisition

ElectricalSeries

starting_time: 0.0

rate: 4800.0

resolution: -1.0

comments: no comments

description: The EEG signals from one electrode amplified 8000-10000 times, lowpass-filtered at 500 Hz (single pole), and stored at 4800 Hz (16 bits/sample).

conversion: 1e-06

offset: 0.0

unit: volts

data

HDF5 dataset

Data type	float64
Shape	(2880000,)
Array size	21.97 MiB
Chunk shape	(5625,)
Compression	gzip
Compression opts	4
Compression ratio	1.5867117300143878

starting_time_unit: seconds

electrodes

description: all electrodes

table

description: metadata about extracellular electrodes

table

	location	group	group_name
id
0	MEC	ElectrodeGroup pynwb.ecephys.ElectrodeGroup at 0x5172750592\nFields:\n description: The name of the ElectrodeGroup this electrode is a part of.\n device: EEG pynwb.device.Device at 0x5173492000\nFields:\n description: The device used to record EEG signals.\n\n location: MEC\n	ElectrodeGroup

keywords

HDF5 dataset

Data type	object
Shape	(3,)
Array size	24.00 bytes
Chunk shape	None
Compression	None
Compression opts	None
Compression ratio	0.5

[b'medial entorhinal cortex' b'spike times' b'position']

processing

behavior

description: Processed behavioral data.

data_interfaces

Position

spatial_series

SpatialSeriesLED1

resolution: -1.0

comments: no comments

description: Position (x, y) for the first tracking LED.

conversion: 0.01

offset: 0.0

unit: meters

data

HDF5 dataset

Data type	float64
Shape	(30000, 2)
Array size	468.75 KiB
Chunk shape	(1875, 1)
Compression	gzip
Compression opts	4
Compression ratio	1.0575039821634329

timestamps

HDF5 dataset

Data type	float64
Shape	(30000,)
Array size	234.38 KiB
Chunk shape	(1875,)
Compression	gzip
Compression opts	4
Compression ratio	3.5103115401491882

timestamps_unit: seconds

interval: 1

reference_frame: (0,0) is not known.

ecephys

description: Processed electrical series data.

data_interfaces

LFP

electrical_series

ElectricalSeriesLFP

starting_time: 0.0

rate: 250.0

resolution: -1.0

comments: no comments

description: The EEG signals from one electrode stored at 250 Hz.

conversion: 1e-06

offset: 0.0

unit: volts

data

HDF5 dataset

Data type	float64
Shape	(150000,)
Array size	1.14 MiB
Chunk shape	(2344,)
Compression	gzip
Compression opts	4
Compression ratio	4.069783216214017

starting_time_unit: seconds

electrodes

description: all electrodes

table

description: metadata about extracellular electrodes

table

	location	group	group_name
id
0	MEC	ElectrodeGroup pynwb.ecephys.ElectrodeGroup at 0x5172750592\nFields:\n description: The name of the ElectrodeGroup this electrode is a part of.\n device: EEG pynwb.device.Device at 0x5173492000\nFields:\n description: The device used to record EEG signals.\n\n location: MEC\n	ElectrodeGroup

electrodes

description: metadata about extracellular electrodes

table

	location	group	group_name
id
0	MEC	ElectrodeGroup pynwb.ecephys.ElectrodeGroup at 0x5172750592\nFields:\n description: The name of the ElectrodeGroup this electrode is a part of.\n device: EEG pynwb.device.Device at 0x5173492000\nFields:\n description: The device used to record EEG signals.\n\n location: MEC\n	ElectrodeGroup

electrode_groups

ElectrodeGroup

description: The name of the ElectrodeGroup this electrode is a part of.

location: MEC

device

description: The device used to record EEG signals.

devices

EEG

description: The device used to record EEG signals.

subject

age: P3M/P5M

age__reference: birth

description: A Long Evans rat.

sex: M

species: Rattus norvegicus

subject_id: 10073

weight: 0.35/0.45

units

description: Autogenerated by NWBFile

waveform_unit: volts

table

	unit_name	spike_times	histology	hemisphere	depth
id
0	t1c1	[0.7903958333333333, 0.794, 0.8111666666666667, 0.8313541666666666, 0.9217708333333333, 1.0205208333333333, 1.3573020833333334, 1.6583229166666666, 1.6768645833333333, 2.7457708333333333, 4.008697916666667, 4.01678125, 4.402270833333334, 4.522583333333333, 4.527708333333333, 5.598760416666667, 5.61415625, 5.617927083333333, 5.68934375, 5.701510416666666, 5.714885416666666, 5.71740625, 5.723197916666667, 5.806802083333333, 5.8149375, 5.8207708333333334, 6.1641875, 6.201979166666667, 6.2260625, 6.2363125, 6.3546875, 6.363916666666666, 6.480145833333333, 6.48803125, 6.899927083333333, 6.992489583333334, 6.995885416666667, 7.033135416666667, 7.098052083333333, 7.10146875, 7.105677083333333, 7.245541666666667, 11.069739583333334, 11.499979166666666, 11.5111875, 11.522375, 11.6165, 11.702270833333333, 11.714625, 11.7245, 11.920979166666667, 11.983385416666666, 11.98634375, 11.995645833333333, 12.08903125, 12.105385416666667, 12.148697916666666, 12.157114583333334, 12.165864583333333, 13.123729166666667, 13.206645833333333, 13.224875, 13.232479166666666, 13.362927083333334, 13.40890625, 13.522697916666667, 13.530177083333333, 13.54115625, 13.623927083333333, 13.685302083333333, 13.738260416666666, 13.757302083333334, 13.812510416666667, 13.855427083333334, 13.971072916666667, 13.98659375, 13.992822916666666, 14.082979166666666, 14.162229166666666, 14.165541666666666, 14.394229166666667, 14.397375, 14.488708333333333, 14.492708333333333, 14.500604166666667, 14.547833333333333, 14.563979166666666, 14.5875, 14.590729166666666, 14.59375, 14.601708333333333, 14.608729166666667, 14.620083333333334, 14.647083333333333, 14.699260416666666, 14.70190625, 14.741635416666666, 14.801010416666667, 14.80403125, 14.88940625, ...]	MEC LII		0.0024
1	t2c1	[1.0451354166666667, 1.7003854166666668, 2.3154375, 11.046822916666667, 14.239729166666667, 14.822927083333333, 14.837010416666667, 19.281322916666667, 19.585395833333333, 19.603958333333335, 19.719083333333334, 19.722625, 19.819458333333333, 19.822979166666666, 19.8256875, 19.829520833333333, 28.67203125, 29.932614583333333, 30.8508125, 30.951416666666667, 31.050583333333332, 31.106822916666665, 31.410760416666665, 36.44560416666667, 46.90858333333333, 47.34158333333333, 47.397375, 47.4190625, 47.47598958333333, 48.156, 59.66520833333333, 59.66970833333333, 59.78719791666666, 60.00934375, 60.12197916666667, 60.12890625, 60.458333333333336, 60.8745625, 61.55807291666667, 62.76680208333333, 62.94321875, 63.27045833333333, 63.4875, 64.47296875, 67.56085416666667, 67.57622916666666, 67.72179166666666, 67.72525, 67.80897916666666, 67.814625, 67.8276875, 67.91458333333334, 67.94144791666666, 67.95988541666667, 68.02155208333333, 68.13059375, 68.20140625, 68.33521875, 68.40710416666667, 68.57409375, 68.58878125, 68.681375, 68.70475, 68.75991666666667, 68.832625, 68.9400625, 68.94379166666667, 71.02867708333333, 71.25821875, 71.41845833333333, 72.28534375, 78.7965, 79.7308125, 79.76083333333334, 79.84297916666667, 79.91891666666666, 79.97095833333333, 80.08979166666667, 83.240875, 88.275625, 91.66017708333334, 91.67665625, 92.069125, 92.10191666666667, 92.56378125, 92.56932291666666, 92.57228125, 92.58971875, 92.59544791666667, 92.67121875, 92.67442708333333, 92.81330208333334, 92.84265625, 93.16694791666667, 93.28475, 93.47997916666667, 93.49264583333333, 93.51422916666667, 93.51847916666667, 93.52220833333334, ...]	MEC LII		0.0024
2	t2c3	[0.18273958333333334, 0.5340729166666667, 0.5707291666666666, 0.7023333333333334, 0.7242604166666666, 0.7670520833333333, 0.88084375, 1.06084375, 1.1815, 1.2828333333333333, 1.2922916666666666, 1.4162291666666667, 1.5238333333333334, 1.5430416666666666, 1.5909479166666667, 1.6242291666666666, 1.6451041666666666, 1.7132604166666667, 3.0415729166666665, 5.295635416666666, 5.516947916666667, 6.2452604166666665, 6.336885416666667, 6.6401666666666666, 7.0116875, 7.089395833333334, 7.20128125, 8.1189375, 8.1546875, 8.251333333333333, 8.605614583333333, 10.502302083333333, 10.848864583333333, 10.931302083333334, 11.852802083333334, 11.86840625, 11.877864583333333, 11.963645833333333, 13.12328125, 13.53028125, 13.688145833333333, 13.751333333333333, 14.159802083333334, 16.810760416666668, 16.91994791666667, 17.323583333333332, 17.454822916666668, 19.2395, 19.306625, 19.73028125, 21.200885416666665, 21.439739583333335, 22.102395833333333, 22.926447916666667, 23.722489583333335, 23.85609375, 25.524104166666667, 25.860020833333333, 26.32103125, 26.6210625, 26.66503125, 26.753708333333332, 26.846958333333333, 26.8845, 26.959229166666667, 27.08540625, 27.1913125, 27.271979166666668, 27.31240625, 27.537260416666665, 27.791447916666666, 27.805697916666666, 27.817010416666665, 27.90071875, 27.917572916666668, 28.02446875, 28.13378125, 28.15521875, 28.32228125, 28.363958333333333, 28.38533333333333, 28.608604166666666, 28.6311875, 29.11065625, 30.226875, 33.932625, 34.056666666666665, 34.590354166666664, 36.890760416666666, 38.448458333333335, 38.4585, 38.78067708333333, 39.00878125, 39.022072916666666, 39.23472916666667, 39.24640625, 39.25477083333333, 39.60910416666667, 40.26836458333333, 40.29759375, ...]	MEC LII		0.0024
3	t3c1	[1.0358229166666666, 1.04803125, 1.6964270833333333, 1.7780416666666667, 1.7842083333333334, 1.8619166666666667, 1.8659375, 1.879125, 1.8885416666666666, 1.9763333333333333, 2.0486666666666666, 2.1341875, 2.1698541666666666, 2.2325416666666666, 2.245875, 2.251375, 2.2590625, 2.2775833333333333, 2.282395833333333, 2.2996041666666667, 2.3334375, 2.3404375, 2.3472708333333334, 2.3584375, 2.380541666666667, 2.3935104166666665, 2.40184375, 2.4201979166666665, 2.44096875, 2.45184375, 2.4599270833333335, 2.4681770833333334, 2.4746770833333334, 2.4855729166666665, 2.5209479166666666, 2.55503125, 2.5716979166666665, 2.5834895833333333, 2.591552083333333, 2.6127604166666667, 2.6709895833333333, 2.88928125, 3.134916666666667, 3.2006875, 3.3154375, 3.4335625, 4.24340625, 4.2707395833333335, 4.34684375, 14.862104166666667, 15.2978125, 15.543479166666666, 16.012020833333334, 16.19559375, 16.322864583333335, 16.855166666666666, 16.8641875, 19.730333333333334, 19.756604166666666, 19.76535416666667, 19.8773125, 19.9308125, 20.047833333333333, 20.227822916666668, 20.318989583333334, 20.336260416666665, 20.47409375, 20.584364583333333, 20.78321875, 20.79134375, 20.810072916666666, 20.824833333333334, 20.8931875, 20.906208333333332, 20.918354166666667, 20.9286875, 21.020104166666666, 21.109541666666665, 21.1209375, 21.129208333333334, 21.139520833333332, 28.955604166666667, 28.969427083333333, 29.12302083333333, 29.227, 29.93634375, 30.745760416666666, 30.862416666666668, 33.691541666666666, 33.70033333333333, 33.70483333333333, 45.592125, 48.75952083333333, 52.425875, 52.44083333333333, 53.031697916666666, 53.03701041666667, 57.72391666666667, 57.736291666666666, 57.74427083333333, ...]	MEC LII		0.0024

... and 4 more rows.

experiment_description: The sample includes conjunctive cells and head direction cells from layers III and V of medial entorhinal cortex and have been published in Sargolini et al. (Science, 2006).

session_id: 17010302

lab: Moser

institution: Centre for the Biology of Memory, Norwegian University of Science and Technology

Access metadata

First, let’s take a look at the metadata in this file.

subject is an attribute of the nwbfile. It holds information about the experimental subject, such as age (in ISO 8601 Duration format), sex, and species in latin binomial nomenclature.

Tasks:

1. Inspect the subject field. If you need a reminder for how to do this, see Step 3 in Lesson 1.

2. Take a look at other attributes of nwbfile as well. Hint: you can hit ‘tab’ after nwbfile. to see all of the attributes and methods of the nwbfile object.

# Look at subject here

Accessing behavior data

The “behavior” processing module holds the behavior data in the NWB file which can be accessed as nwbfile.processing["behavior"].

Position

“Position” gives us the location of the mouse in space. The position data is stored in a SpatialSeries object which can be accessed from the “Position” container as nwbfile.processing["behavior"]["Position"].

Task: Look at the original paper. How did the researchers figure out the position of the animal?

Note that not all sessions have position data from two tracking LEDs.

spatial_series = nwbfile.processing["behavior"]["Position"]["SpatialSeriesLED1"]

# Inspect conversion and data
print(spatial_series.conversion)
print(spatial_series.data)

0.01
<HDF5 dataset "data": shape (30000, 2), type "<f8">

Now that we have the behavioral data, we can plot it. The conversion field tells us how to translate the values in data to meters. The data object here has 3,000 entries for x positions (at index 0) and y positions (at index 1). So, the first thing we’ll do is convert the data into meters, and then we can plot it.

import matplotlib.pyplot as plt

# Extract & convert x and y positions
x =spatial_series.data[:, 0] * spatial_series.conversion
y =spatial_series.data[:, 1] * spatial_series.conversion

# Plot and label!
fig, ax = plt.subplots(1,1,figsize=(4,4))
plt.plot(x,y)
plt.xlabel('X (meters)')
plt.ylabel('Y (meters)')
plt.show()

Accessing spike times

As a reminder, the Units table holds the spike times which can be accessed as nwbfile.units and can also be converted to a pandas DataFrame.

Task: Access units below and convert it to a dataframe. Assign this to units_df. If you need a reminder for how to do this, refer back to Lesson 1. Inspect the entire dataframe.

nwbfile.units.to_dataframe()

	unit_name	spike_times	histology	hemisphere	depth
id
0	t1c1	[0.7903958333333333, 0.794, 0.8111666666666667...	MEC LII		0.0024
1	t2c1	[1.0451354166666667, 1.7003854166666668, 2.315...	MEC LII		0.0024
2	t2c3	[0.18273958333333334, 0.5340729166666667, 0.57...	MEC LII		0.0024
3	t3c1	[1.0358229166666666, 1.04803125, 1.69642708333...	MEC LII		0.0024
4	t3c2	[2.43025, 2.4398333333333335, 3.17965625, 3.39...	MEC LII		0.0024
5	t3c3	[2.1157708333333334, 2.425427083333333, 3.3630...	MEC LII		0.0024
6	t3c4	[0.07945833333333334, 2.244947916666667, 3.173...	MEC LII		0.0024
7	t4c1	[2.4301666666666666, 2.439770833333333, 3.1795...	MEC LII		0.0024

(Site note: for an interactive visualization of spike times and position, try out Neurosift.

Visualizing rate maps

As you can see in the dataframe above, there are 8 recorded neurons (indices 0 through 7) in this dataset. This section demonstrates how to show the rate maps of those recorded cells. We will use PYthon Neural Analysis Package (pynapple) to calculate the rate maps. The first cell will install pynapple.

try:
    import pynapple  
    print('pynapple imported.')
    
except ImportError as e:
    !pip install pynapple

pynapple imported.

Using the compute_2d_tuning_curves() function from pynapple (imported above as nap), we can compute firing rate as a function of position (map of neural activity as the animal explored the environment).

import pynapple as nap

# Compute position over time
position_over_time = nap.TsdFrame(
    d=spatial_series.data[:],
    t=spatial_series.timestamps[:],
    columns=["x","y"],
)

spike_times_group = nap.TsGroup({cell_id: nap.Ts(spikes) for cell_id, spikes in enumerate(nwbfile.units["spike_times"])})

num_bins = 15

rate_maps, position_bins = nap.compute_2d_tuning_curves(
    spike_times_group,
    position_over_time,
    num_bins,
)

print(type(rate_maps))
print(len(rate_maps))

<class 'dict'>
8

The rate_maps object generated above is a dictionary, in which each entry’s key is the unit ID, and the value is the rate map.

Task: Using plt.imshow(), look at a few rate maps! As a reminder, you can extract the value of a dictionary using the syntax dictionary_name[key].

fig, ax = plt.subplots(1,1,figsize=(4,4))

# Plot a rate map or two here!

Visualizing grid cells activity

To determine whether the firing fields of individual cells formed a grid structure, we will calculate the spatial autocorrelation for the rate map of each cell.

The autocorrelograms are based on Pearson’s product moment correlation coefficient with corrections for edge effects and unvisited locations. With λ (x, y) denoting the average rate of a cell at location (x, y), the autocorrelation between the fields with spatial lags of τx and τy was estimated as:

where the summation is over all n pixels in λ (x, y) for which rate was estimated for both λ (x, y) and λ (x - τx, y - τy). Autocorrelations were not estimated for lags of τx, τy where n < 20.

The degree of spatial periodicity (gridness) can be determined for each cell by rotating the autocorrelation map for each cell in steps of 6 degrees (from 0 to 180 degrees) and computing the correlation between the rotated map and the original. The correlation is confined to the area defined by a circle around the peaks that are closest to the centre of the map, and the central peak is not included in the analysis.

The ‘gridness’ of a cell can be expressed as the difference between the lowest correlation at 60 and 120 degrees (where a peak correlation would be expected due to the triangular nature of the grid) and the highest correlation at 30, 90, and 150 degrees (where the minimum correlation would be expected). When the correlations at 60 and 120 degrees of rotation exceeded each of the correlations at 30, 90 and 150 degrees (gridness > 0), the cell was classified as a grid cell.

First, let’s define our functions to help us make these calculations.

import numpy as np

def create_coer_arr(arr, rad_min=None, rad_max=None):
    """ Creating an array for correlation(tau_x, tau_y)
    Takes tau_x from the range (-arr.shape[0]+1, arr.shape[0]-1) and the same for tau_y
    """
    sh_x, sh_y = arr.shape
    # creating an array full of nan's
    coer_arr = np.full((2*sh_x-1, 2*sh_y-1), np.nan)
    for ii in range(0, 2*(sh_x-1)):
        for jj in range(0, 2*(sh_y-1)):
            # shifting tau_x/y
            tau_x = ii-sh_x+1
            tau_y = jj-sh_y+1
            # if rad_max and rad_min is provided, I only calculate the correlation for points between rad_min and rad_max
            if rad_max is not None and ((tau_x**2 + tau_y**2)**0.5 > rad_max):
                continue
            if rad_min is not None and ((tau_x**2 + tau_y**2)**0.5 < rad_min):
                continue
            coer_arr[ii, jj] = pearson_autocor(arr, lag_x=tau_x, lag_y=tau_y)
    return coer_arr

def pearson_autocor(arr, lag_x, lag_y):
    """ Calculates Pearson autocorrelation for an array that can contain NaN values."""
    sh_x, sh_y = arr.shape
    if abs(lag_x) >= sh_x or abs(lag_y) >= sh_y:
        raise Exception(f"abs(lag_x), abs(lag_y) have to be smaller than {sh_x}, {sh_y}, but {lag_x}, {lag_y} provided")

    # calculating sum for elements that meet the requirements
    n = 0
    sum1, sum2, sum3, sum4, sum5 = 0, 0, 0, 0, 0
    for ii in range(0, sh_x):
        for jj in range(0, sh_y):
            # checking if the indices are withing the array
            if 0 <= ii-lag_x < sh_x and 0 <= jj-lag_y < sh_y:
                # checking if both values (in ii,jj and shifted) are not nan
                if not np.isnan(arr[ii, jj]) and not np.isnan(arr[ii-lag_x, jj-lag_y]):
                    
                    n += 1
                    sum1 += arr[ii, jj] * arr[ii-lag_x, jj-lag_y]
                    sum2 += arr[ii, jj] 
                    sum3 += arr[ii-lag_x, jj-lag_y]
        
                    sum4 += (arr[ii, jj])**2
                    sum5 += (arr[ii-lag_x, jj-lag_y])**2

              
    # according to the paper they had this limit for number of points
    if n < 20:
        return np.nan

    numerator = n * sum1 - sum2 * sum3
    denominator = (n * sum4 - sum2**2)**0.5 * (n * sum5 - sum3**2)**0.5
    cor = numerator / denominator

    return cor

def pearson_cor_2arr(arr1, arr2):
    """ Calculates Pearson correlation for two arrays with the same shape and no NaN."""
    if not arr1.shape == arr2.shape:
        raise Exception("Both arrays should have the same shape")
    n = arr1.shape[0] * arr1.shape[1]
 
    numerator = n * np.sum(arr1 * arr2) - np.sum(arr1) * np.sum(arr2)
    denominator = (n * np.sum(arr1**2) - np.sum(arr1)**2)**0.5 * (n * np.sum(arr2**2) - np.sum(arr2)**2)**0.5
    return numerator / denominator

%whos

Variable             Type                 Data/Info
---------------------------------------------------
CachingFileSystem    _Cached              <class 'fsspec.implementa<...>ached.CachingFileSystem'>
DandiAPIClient       type                 <class 'dandi.dandiapi.DandiAPIClient'>
File                 ABCMeta              <class 'h5py._hl.files.File'>
NWBHDF5IO            ABCMeta              <class 'pynwb.NWBHDF5IO'>
asset                RemoteBlobAsset      DANDI:assets/2b9e441b-56bc-4be2-893e-0e02d22d239d
ax                   Axes                 Axes(0.125,0.11;0.775x0.77)
client               DandiAPIClient       <dandi.dandiapi.DandiAPIC<...>nt object at 0x107a23440>
create_coer_arr      function             <function create_coer_arr at 0x30a3ff9c0>
dandiset_id          str                  000582
fig                  Figure               Figure(400x400)
file                 File                 <HDF5 file "26a22c31-09bc<...>-edc7394ed12c>" (mode r)>
file_system          HTTPFile             <File-like object HTTPFil<...>c-43a4-9187-edc7394ed12c>
filesystem           function             <function filesystem at 0x1247ac4a0>
fs                   CachingFileSystem    <fsspec.implementations.c<...>em object at 0x1268338f0>
io                   NWBHDF5IO            <pynwb.NWBHDF5IO object at 0x1345b3ad0>
nap                  module               <module 'pynapple' from '<...>es/pynapple/__init__.py'>
np                   module               <module 'numpy' from '/op<...>kages/numpy/__init__.py'>
num_bins             int                  15
nwbfile              NWBFile              root pynwb.file.NWBFile a<...>ass 'pynwb.misc.Units'>\n
nwbfile_path         str                  sub-10073/sub-10073_ses-1<...>0302_behavior+ecephys.nwb
pearson_autocor      function             <function pearson_autocor at 0x30a3ff880>
pearson_cor_2arr     function             <function pearson_cor_2arr at 0x30a3ff4c0>
plt                  module               <module 'matplotlib.pyplo<...>es/matplotlib/pyplot.py'>
position_bins        list                 n=2
position_over_time   TsdFrame             Time (s)    x         y\n<...>loat64, shape: (30000, 2)
pynapple             module               <module 'pynapple' from '<...>es/pynapple/__init__.py'>
rate_maps            dict                 n=8
s3_url               str                  https://dandiarchive.s3.a<...>bc-43a4-9187-edc7394ed12c
spatial_series       SpatialSeries        SpatialSeriesLED1 pynwb.b<...>seconds\n  unit: meters\n
spike_times_group    TsGroup                Index     rate\n-------<...> 2.8855\n      7  1.46525
x                    ndarray              30000: 30000 elems, type `float64`, 240000 bytes (234.375 kb)
y                    ndarray              30000: 30000 elems, type `float64`, 240000 bytes (234.375 kb)

Now that we have these functions, let’s use them to analyze the data. There’s a lot of code below and it uses a new package plotly for interactive plotting – don’t worry about the code, just the figures it creates.

First, let’s make sure plotly is installed:

try:
    import plotly
    print('plotly installed.')
except ImportError as e:
    !pip install plotly

plotly installed.

import plotly.express as px
from plotly.subplots import make_subplots
import plotly.graph_objects as go
from scipy.ndimage import rotate
import scipy

rate_maps_50_bin, _ = nap.compute_2d_tuning_curves(
    spike_times_group,
    position_over_time,
    50,
)

for cell_ind in range(len(rate_maps)):
    unit_name = nwbfile.units["unit_name"][cell_ind]
    fig = make_subplots(
        rows=1,
        cols=3,
        subplot_titles=(f'{unit_name} rate map', f'{unit_name} auto-correlation', "periodicity"),
    )

    rate_map_plot = go.Heatmap(z=rate_maps[cell_ind], colorscale='Viridis', showscale=False)
    fig.add_trace(rate_map_plot, row=1, col=1)

    # Compute auto-correlation
    autocorr = create_coer_arr(rate_maps_50_bin[cell_ind], rad_max=34, rad_min=6)
    autocorr_nonan = np.nan_to_num(autocorr, copy=True, nan=0.0)

    correlations = []
    angles = np.arange(0, 186, 6)
    for angle in angles:
        autocorr_nonan_rotated = rotate(autocorr_nonan, angle=angle, reshape=False)
        cor = pearson_cor_2arr(autocorr_nonan_rotated, autocorr_nonan)
        correlations.append(cor)
    
    gridness = max(correlations[10], correlations[20]) - max(correlations[5], correlations[15], correlations[25])
    gridness = np.round(gridness, 2)
    
    autocorr_rate_map = go.Heatmap(z=autocorr, colorscale='Viridis', showscale=False)
    fig.add_trace(autocorr_rate_map, row=1, col=2)
    
    line_trace = go.Scatter(
        x=angles,
        y=correlations,
        mode='lines',
        marker=dict(color="black"),
        
    )
    
    fig.add_trace(line_trace, row=1, col=3)

    fig.update_xaxes(showticklabels=False)
    fig.update_yaxes(showticklabels=False)
    
    fig.update_xaxes(showticklabels=True, row=1, col=3, title_text="Rotation (deg)")
    fig.update_yaxes(showticklabels=True, row=1, col=3, title_text="Correlation (r)")
    
    fig.update_layout(
        title=f"Gridness score {gridness}",
        xaxis3 = dict(
            tickmode="array",
            tickvals=[30, 60, 90, 120, 150, 180],
        )
    )

    fig.show()

/opt/miniconda3/lib/python3.12/site-packages/pynapple/process/tuning_curves.py:269: RuntimeWarning: invalid value encountered in divide
  count = count / occupancy

As you can see most cells could be classified as “grid cells”, the auto-correlation maps look good and they have high periodicity, i.e., there is clear sinusoidal behavior of the periodicity function with clear maximums around 0, 60, 120 and 180 deg. However, one example (t3c4) doesn’t have clear autocorrelation and the periodicity function has no sinusoidal behavior.